My favourite "only a few hours" which can be easily stretched or shrunk is to get the Tube to HAMMERSMITH, walk 10 feet across platform & get a Tube to WESTMINSTER, use the BRIDGE STREET exit and look up.

Then you can cross the river to the London Eye, walk back across the river by the next bridge downstream and up to Trafalgar Square. Then walk down Whitehall to House Guards (stroke horse, do not stroke shiny man) past Downing Street and then take the lane to the Cabinet War Rooms / Churchill Museum.

You can then walk up Birdcage Walk or through St James's Park to Buckingham Palace then to Victoria where you get the Tube to Hammersmith, then walk 10 ft across the platform to get the Tube back to Heathrow.

Alternatives for a wet day are Tube to South Kensington & the underground walkway to the Museums or Tube to Holborn and walk a few hundred yards to the British Museum

See Central London Map - it prints to A4 size quite well